Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 161, pp. 1-13.

Title: Existence of solutions and convergence results for dynamic
       initial value problems using lower and upper solutions.
       
Author: Atiya H. Zaidi (Univ. of New South Wales, Sydney, Australia)

Abstract:
 In this article, we study the existence of solutions to first
 order non-linear initial value problems within the field of
 "dynamic equations on time scales".
 We employ the method of upper and lower solutions and Schauder's
 fixed point theorem. We also provide sufficient conditions
 under which the upper and lower solutions converge uniformly
 to a solution. Some examples are given to illustrate the 
 new results.

Submitted November 24, 2009. Published December 17, 2009.
Math Subject Classifications: 34N05, 26E70.
Key Words: Existence of solutions; non-linear nabla equations;
           lower and upper solutions; zero approximations.